A rectangular pyramid and a rectangular prism have the same base measurements and
height measurements. If the volume of the prism is 30 cubic inches,
what is the volume of the pyramid? To check if you answer is
reasonable, think about which shape is bigger.

9514 1404 393

  10 cubic inches

Step-by-step explanation:

The volume of of a prism is 3 times the volume of a pyramid with the same base area and height.

  pyramid volume = 1/3(prism volume)

  pyramid volume = (1/3)(30 in³) = 10 in³

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions